Dehn Surgery on Knots in 3-manifolds

  title={Dehn Surgery on Knots in 3-manifolds},
  author={Marc Lackenby},
It has been known for over 30 years that every closed connected orientable 3manifold is obtained by surgery on a link in S [8]. However, a classification of such 3-manifolds in terms of this surgery construction has remained elusive. This is due primarily to the lack of uniqueness of the surgery description. In [5], Kirby gave us a calculus of surgery diagrams. However, the lack of a ‘canonical’ surgical method of getting from one 3-manifold to another has hampered further progress. In this… CONTINUE READING

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Sutured manifolds and generalized Thurston norms

  • M. Scharlemann
  • J. Differ. Geom
  • 1989
Highly Influential
9 Excerpts

Lectures on Three-Manifold Topology, Regional Conference Series in Mathematics, No

  • W. Jaco
  • Providence
  • 1980
Highly Influential
10 Excerpts

MR 54:3702 License or copyright restrictions may apply to redistribution; see

  • J. Hempel, 3-Manifolds, Ann
  • Math. Studies,
  • 1976
Highly Influential
3 Excerpts

Only integral Dehn surgeries yield reducible manifolds, Math

  • C. Gordon, J. Luecke
  • Proc. Camb. Phil. Soc
  • 1987
1 Excerpt

The geometries of 3-manifolds

  • P. Scott
  • Bull. London Math. Soc
  • 1983
1 Excerpt

A calculus for framed links in S3

  • R. Kirby
  • Inv. Math
  • 1978
1 Excerpt

A representation of orientable combinatorial 3 - manifolds

  • W. B. R. Lickorish
  • Inv . Math .
  • 1978

Lickorish, A representation of orientable combinatorial 3-manifolds

  • B R.W.
  • Ann. of Math
  • 1962
1 Excerpt

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